Question

In the given figure, ABCD is a cyclic quadrilateral whose side CD
has been produced to E. If BA
BC and BAC = 40°, find ADE.
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Answer 1

Answer:

the question was not very clear,anyways I have attached my answer..hope it is correct and it helps...

Answer 2

The value of angle ADE is 100°

Step-by-step explanation:

Given:

Quadrilateral ABCD is a cyclic quadrilateral

∠CAB= 40°

∠ACB= 40°

To find:

measure of ∠ADE

Solution:

We know that ABCD is a cyclic quadrilateral

Consider the ΔABC,

where the m∠CAB= 40°, m∠ACB= 40°........(from given)

∠CAB + ∠CBA+ ∠ACB = 180°= ..(sum of measures of a triangle is 180°)

∴40°+∠CBA+ 40°=180°

∴ ∠CBA+ 80°= 180°

∴ ∠CBA= 100°

According to the cyclic quadrilateral theorem

∠CBA+ ∠CDA=180°....(opposite angles of a cyclic quadrilateral are

                                                        supplementary)

100°+ ∠CDA=180°

∴ ∠CDA =80°

∠CDA & ∠ADE are in linear pair

∴ ∠CDA+∠ADE = 180°...(sum of angles in linear pair is 180°)

80°+∠ADE= 180°

So we get, m∠ADE= 100°

Thus, the measure of angle ADE is 100°